Commentary on Theories of Mathematics Education

422 D. Tirosh and P. Tsamir
The teacher will decide whether to set a new goal on the basis of what he or she believes is
important at the moment. If a new high-priority goal is established, the teacher will search
through his or her knowledge base for actions to meet that goal (and perhaps other high
priority goals as well). This results in a change of direction, with a new top-level goal.
(p. 495)
In a series of papers, Schoenfeld and the other members of the Teacher Model Group
used the Teaching-In-Context theory to model various sets of tutoring and teaching
episodes. They reported that evidence from the range of cases that have been
modeled suggests that the underlying architecture of the model and of the Teaching-
In-Context theory are robust, that is, that teachers’ decision-making and problemsolving
are a function of the teachers’ knowledge, goals, and beliefs (Arcavi and
Schoenfeld 1992; Schoenfeld 1998, 1999, 2000, 2002, 2003, 2006; Schoenfeld et
al. 2000).
The Teaching-In-Context theory, like many theories in mathematics education,
was developed in a certain setting. The issue of generality, or scope, of this theory,
namely, the question: “How widely does this theory actually apply?” is a central
issue with regard to any theory in mathematics education, including the Teaching-
In-Context theory. A major aim of the Teacher Model Group, at Berkely, has been
to move toward modeling of increasingly complex behavior in various situations,
starting from problem solving in a laboratory, then in tutoring, then in teaching.
Testing the relevance of the Teaching-In-Context theory in various situations could
significantly contribute to determining its realm of application.
In Törner, Rolka, Rösken and Sriraman’s chapter: “Understanding a teacher’s
actions in the classroom by applying Schoenfeld’s theory Teaching-In-Context:Reflecting
on goals and beliefs”, the scene takes place in a mathematics, Grade 8 class
in a gymnasium in Germany. The chapter focuses on an unexpected turning point
in a lesson that was thoroughly prepared by an experienced teacher (an interesting
case of Situation 2). Törner, Rolka, Rösken and Sriraman describe and discuss their
attempts to examine the teacher’s unanticipated action through the lens of Schoenfeld’s
theory.
The specific situation that is described in Törner et al.’s chapter is different, in
many aspects, from the situations that were previously analyzed by the Teacher
Model Group: The study is conducted in Germany (the other studies were conducted
in the United States); The school culture has specific characteristic (gymnasium);
The study is conducted in Grade 8 by a teacher that is not involved in
research in mathematics education; The circumstances of the lesson are unusual.
The teacher volunteered to video-record her lesson, to be used in a bi-national inservice
teacher training organized by the University of Duisburg-Essen in Germany
and the Freudenthal Institute in the Netherlands. The teacher frequently attended inservice
teaching training courses, in particular on using computer algebra systems
and open tasks in mathematics education. This setting provides an opportunity to
test the application of the Teaching-In-Context theory in a setting that had not examined
before. Thus, this chapter has a potential of offering valuable information
about the generality of the Teaching-In-Context theory.
Törner et al.’s chapter testifies to the applicability of the Teaching-In-Context
theory to the classroom situation that is described in the chapter. This application